Cooperative and Noncooperative Multi-Level Programming

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Springer Science & Business Media, Jun 18, 2009 - Business & Economics - 250 pages
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To derive rational and convincible solutions to practical decision making problems in complex and hierarchical human organizations, the decision making problems are formulated as relevant mathematical programming problems which are solved by developing optimization techniques so as to exploit characteristics or structural features of the formulated problems. In particular, for resolving con?ict in decision making in hierarchical managerial or public organizations, the multi level formula tion of the mathematical programming problems has been often employed together with the solution concept of Stackelberg equilibrium. However,weconceivethatapairoftheconventionalformulationandthesolution concept is not always suf?cient to cope with a large variety of decision making situations in actual hierarchical organizations. The following issues should be taken into consideration in expression and formulation of decision making problems. Informulationofmathematicalprogrammingproblems,itistacitlysupposedthat decisions are made by a single person while game theory deals with economic be havior of multiple decision makers with fully rational judgment. Because two level mathematical programming problems are interpreted as static Stackelberg games, multi level mathematical programming is relevant to noncooperative game theory; in conventional multi level mathematical programming models employing the so lution concept of Stackelberg equilibrium, it is assumed that there is no communi cation among decision makers, or they do not make any binding agreement even if there exists such communication. However, for decision making problems in such as decentralized large ?rms with divisional independence, it is quite natural to sup pose that there exists communication and some cooperative relationship among the decision makers.
 

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Contents

Introduction
1
12 Description of contents
6
Optimization Concepts and Computational Methods
10
22 Multiobjective programming
13
222 Interactive multiobjective programming
14
223 Fuzzy multiobjective programming
16
23 Stochastic programming
17
24 Genetic algorithms
20
442 Numerical example
119
45 Fuzzy decentralized twolevel linear programming
121
451 Interactive fuzzy programming
122
452 Numerical example
127
46 Fuzzy twolevel linear 01 programming
132
461 Interactive fuzzy programming
133
462 Genetic algorithm with double strings
134
463 Numerical example
137

Noncooperative Decision Making in Hierarchical Organizations
25
32 Twolevel linear programming
31
322 Computational methods based on genetic algorithms
33
323 Computational Experiments
36
33 Twolevel mixed zeroone programming
38
331 Facility location and transportation problem
39
332 Computational methods based on genetic algorithms
42
333 Computational Experiments
47
34 Twolevel linear integer programming
50
341 Computational methods based on genetic algorithms
52
342 Computational Experiments
56
35 Multiobjective twolevel linear programming
59
351 Computational methods
61
352 Numerical examples
71
36 Stochastic twolevel linear programming
75
361 Stochastic twolevel linear programming models
76
362 Computational method for Vmodel
78
363 Numerical example
80
Cooperative Decision Making in Hierarchical Organizations
83
42 Fuzzy two and multilevel linear programming
86
421 Interactive fuzzy programming for twolevel problem
87
422 Numerical example for twolevel problem
93
423 Interactive fuzzy programming for multilevel problem
97
424 Numerical example for multilevel problem
102
43 Fuzzy twolevel linear programming with fuzzy parameters
106
432 Numerical example
111
44 Fuzzy twolevel linear fractional programming
114
441 Interactive fuzzy programming
115
47 Fuzzy twolevel nonlinear programming
139
471 Interactive fuzzy programming
141
Revised GENOCOP III
146
473 Numerical example
150
48 Fuzzy multiobjective twolevel linear programming
153
481 Interactive fuzzy programming
154
482 Numerical example
161
49 Fuzzy stochastic twolevel linear programming
166
491 Stochastic twolevel linear programming models
167
492 Interactive fuzzy programming
169
493 Numerical example
171
494 Alternative stochastic models
176
Some applications
181
511 Problem formulation
183
512 Maximization of profit
185
513 Maximization of profitability
193
514 Discussions and implementation
200
52 Decentralized twolevel transportation problem
201
521 Problem formulation
202
522 Interactive fuzzy programming
207
53 Twolevel purchase problem for food retailing
223
531 Problem formulation
224
532 Parameter setting and Stackelberg solution
226
533 Sensitivity analysis
231
534 Multistore operation problem
234
References
239
Index
248
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About the author (2009)

Masatoshi Sakawa was born in Matsuyama, Japan on 11 August 1947. He received B.E., M.E., and D.E. degrees in applied mathematics and physics at Kyoto University in 1970, 1972, and 1975, respectively. From 1975 he was with Kobe University where, since 1981, he was an Associate Professor in the Department of Systems Engineering. From 1987 to 1990 he was a Professor in the Department of Computer Science at Iwate University. At present he is a Professor at Hiroshima University and is working with the Department of Artificial Complex Systems Engineering in the Graduate School of Engineering. He was an Honorary Visiting Professor at University of Manchester Institute of Science and Technology (UMIST), Computation Department, sponsored by the Japan Society for the Promotion of Science (JSPS) from March to December 1991. He was also a Visiting Professor at the Kyoto Institute of Economic Research, Kyoto University from April 1991 to March 1992.

His research and teaching activities are in the area of systems engineering, especially mathematical optimization, multiobjective decision making, fuzzy mathematical programming and game theory. In addition to over 300 articles in National and International Journals, he is an author and coauthor of 5 books in English and 14 books in Japanese, including the Springer titles Genetic Algorithms and Fuzzy Multiobjective Optimization; Fuzzy Sets and Interactive Multiobject Optimization; Large-Scale Interactive Fuzzy Multiobjective Programming: Decomposition Approaches; and, with Nishizaki, Fuzzy and Multiobjective Games for Conflict Resolution.

Ichiro Nishizaki was born in Osaka, Japan, in January, 1959. He received B.E. and M.E. degrees in systems engineering at Kobe University in 1982 and 1984, respectively, and he received the D.E. degree from Hiroshima University in 1993. From 1984 to 1990, he worked for Nippon Steel Corporation. From 1990 to 1993, he was a Research Associate at the Kyoto Institute of Economic Research, Kyoto University. From 1993 to 1996, he was an Associate Professor in the Faculty of Business Administration and Informatics at Setsunan University. From 1997 to 2001, he was an Associate Professor at Hiroshima University, and was working with the Department of Artificial Complex Systems Engineering in the Graduate School of Engineering. At present, he is a Professor in that department. His research and teaching activities are in the area of systems engineering, especially game theory, multiobjective decision making, and fuzzy mathematical programming. He is an author or coauthor of about eighty papers, one book in English (Springer: Fuzzy and Multiobjective Games for Conflict Resolution), and two books in Japanese.

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